Townsend is currently on holiday after last week being cut from the England squad that travelled to France for Euro 2016 on Monday.
The Telegraph report Newcastle have indicated they may be prepared to offer the player a £20,000-a-week rise to his £55,000-a-week wages to stay with the club in the Championship.
Palace are willing to give him an £80,000-a-week contract to move back to London just months after his £12million transfer from Tottenham.
Following early teething troubles in the north-east, Townsend emerged as a key figure in Newcastle’s survival bid under Rafael Benitez and his record of four goals in 13 Premier League games for the club was enough to earn him a place in England’s provisional 26-man squad for Euro 2016.